DR. OLIVER LODGE ON ABERRATION PROBLEMS. 
749 
straight, will remain straight in spite of motion ; whatever shape it had, that it will 
retain. Only cos e, and variations in a®, can produce any effect on path, and effects 
so produced must be very small, since the value of cos e is v/(l — a.^ sin^ 6). A 
second-order effect on direction may therefore be produced by irrotational motion, but 
not a first-order effect. A similar statement applies to the time of journey round any 
closed periphery. 
Michelson’s Experiment. 
25. We conclude, therefore, that general ethereal drift does not affect either the 
path of a ray or the time of its journey round a complete contour, to any important 
extent. But that taking second-order quantities into account, the time of going to ' 
and fro in any direction inclined at angle ^ to a constant drift is, from the above 
expression, § 24, 
2 T cos e _ v/(I — siir 6) 
1 0 -I o X -J I, 
1 — a~ i — a- 
where 2T is the ordinary time of the double journey. 
Hence, by this means, interference effects due to drift would seem to be possible, 
since the time depends subordinately on the inclination of ray to drift {cf. §§ 59-62) 
The above expression applies to Michelson’s^ remarkable experiment of sending a 
split beam to and fro, half along and half across the line of earth motion ; and is, in 
fact, the theory of it. There ought to be an effect due to the difference between 
^ = 0 and 6 = 90°, but he does not observe any. Hence, either something else 
happens, or the ether near the earth is dragged with it, so as not to stream through 
our instruments. When a is constant I see no way out of this conclusion, except 
hypothetical disturbance at reflexion of some minute kind, one of the mirrors being 
normal and the other tangential to the drift; but I perceive no adequate reason for 
this suggestion (see § 60). It is true tha.t if the earth is carrying the ether with it, 
a will not be constant, at different distances from its surface ; but, then, the plane of 
Michelson’s experiment was horizontal. 
If the ether is dragged along near moving matter it behaves like a viscous fluid, 
and a velocity-potential must (save by some exceptional theory, § 31) be abandoned ; 
but, as this would involve the curvature of rays striking the earth and much comiili- 
cation, it seems a pity to abandon it until compelled by direct experimental evidence 
to recognize ethereal viscosity. 
The experiment of Michelson’s raises a strong presumption in favour of such 
viscosity, nevertheless his negative result is conceivably explicable in other ways: 
one of which has been ingeniously suggested by Professor Fitzgerald, viz., that the 
cohesion force between molecules, and, therefore, the size of bodies, may be a 
* ‘ PMl. Mag.,’ Dec., 1887. 
